On the homology of low dimensional cohomogeneity one manifolds

TL;DR

This paper characterizes the possible homology groups of compact simply connected cohomogeneity one manifolds in dimensions up to seven, providing a classification of their topological structures.

Contribution

It offers a complete characterization of homology groups for low-dimensional cohomogeneity one manifolds, advancing understanding of their topological properties.

Findings

Homology groups are classified for dimensions up to seven.

Results specify which homology groups can occur in these manifolds.

Provides a foundation for further topological classification of cohomogeneity one manifolds.

Abstract

In this paper we give a characterization of the possible homology groups that can occur for compact simply connected cohomogeneity one manifolds in dimensions seven and lower.